How to show a "visibility: admin only" field in the New Submission email?

Hi there,
I just realized that a field which is set to visibility "admin only", does not show in the "New Submission" email to myself. I am populating the data for that field with a content template, so there should be data in that field (and it shows in the post in WP). Is there a way to show that data for the hidden field in the email?

I guess it depends when the content template is generated? Is there any documentation what happens exactly when a content template is created? Where would I look in the code? Could I use a hook/filter?
Thanks!

Thanks Carl,
could there be a workaround? When is the post created? Before the entry or after? When is the email send? Before the post is created or after? When exactly does the content template fire?

Could I for instance copy the whole content template functionality into my function.php file and use a filter/hook to update that entry field (or even in the DB) before the email is send? Or just send another email and disable the original email functionality?

P.S: How do I find out in which way GF works (like a flow diagramm or something)? When does it send the email, create the post, save the entry in DB, etc...